Evaluate the expression for the given value of x. 3.5x − 3.5 for x = 3

Step-by-step explanation:

Xj + Xk/2 = Xm

7 + Xk/2 = 1

to get rid of the bracket, multiply all two sides by the denominator.

2(7 + Xk/2) = 1(2)

7 + Xk = 2

Xk = 2 - 7

Xk = -5

Yj + Yk/2 = Ym

2 + Yk/2 = -2

to get rid of the bracket, multiply all two sides by the denominator.

2(2 + Yk/2) = -2(2)

2 + Yk = -4

Yk = -4 - 2

Yk = -6

Therefore the coordinates of point K is (-5,-6)

Answer:

Step-by-step explanation:

Basic Charge = $ 65

Rate per hour = $ 28

Number of hours = H

Rate for H hours = 28 *H = 28H

Equation:

65 + 28H ≤ 250

Anan consideration requires:

Requirements of the plumber

Thus, to determine the number of how many hours Anan can afford for his total amount of $250, we have the following:

The initial fee + hourly rate ≤ 250  

∴

   $65 + $28 H ≤ 250

Therefore, we can conclude that the perfect inequality that describes Anan Scenario is:    $65 + $28 H ≤ 250

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Answer:

x          y

10   →   6

4    →    0

8    →    4

Step-by-step explanation:

Using the given rule, plug in any known values:

[tex]y=x-4\\\\6=x-4[/tex]

Solve for x. Add 4 to both sides of the equation to isolate the variable:

[tex]6+4=x-4+4\\\\x=10[/tex]

Repeat:

[tex]y=x-4\\\\0=x-4\\\\0+4=x-4+4\\\\x=4[/tex]

[tex]y=x-4\\\\4=x-4\\\\4+4=x-4+4\\\\x=8[/tex]

:Done

Answer:

  0, 5, 10

Step-by-step explanation:

You can solve the inequality to determine what values to select.

  28 -7x ≤ -4(-7x -7) . . . . . . given

  28 -7x ≤ 28x +28 . . . . . . eliminate parentheses*

  -7x ≤ 28x . . . . . . . . . . . . . subtract 28 from both sides

  0 ≤ 35x . . . . . . . . . . . . . . add 7x to both sides

  0 ≤ x . . . . . . . . . . . . . . . . . divide by 35

So, all values that are 0 or greater will make the inequality true:

  0, 5, 10

_____

* Parentheses are eliminated using the distributive property. The factor outside parentheses multiplies each of the terms inside. Pay attention to signs.

  -4(-7x -7) = (-4)(-7x) +(-4)(-7) = 28x +28

For the smaller triangle, the rise is 2 since this is the length of the vertical component. The horizontal component is 3, meaning the run is 3

Slope = rise/run

Slope = 2/3

---------------

The larger triangle leads to the same slope because

slope = rise/run

slope = 4/6

slope = (2*2)/(2*3)

slope = 2/3

Because we get the same slope value, this confirms that both triangles have their hypotenuse on the same straight line.

The two triangles are similar. The larger triangle's sides are twice as long as its smaller counterpart.

Answer:

Step-by-step explanation:

Slope = 0

The line is parallel to x-axis

Equation: y = 1

y -1 = 0

Answer:

y - 1 = 0

Step-by-step explanation:

As we move from the first point to the second, x increases by 4 (this is the 'run') but y does not change (that is, the 'rise' is zero).  Thus, the slope of the line is 0, and the equation of the line is y = 1, or (equivalently) y - 1 = 0.

The solution is 2 roots

The number of roots the equation will have if the value of the discriminant is 73 will be 2 roots

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the quadratic equation be A

where A = ax² + bx + c=0

Let the discriminant of the equation be D

Now , the value of D = 73

To calculate the number of roots a quadratic equation A

We need to compute the discriminant (b² - 4ac).

If the discriminant is less than 0, then the quadratic has no real roots.

If the discriminant is equal to zero then the quadratic has equal roots.

If the discriminant is more than zero then it has 2 distinct roots.

So , the value of D > 0

Therefore , the equation has 2 roots

Hence , the number of roots of the quadratic equation is 2 roots

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Given that :-

To Find :-

Solution :-

→ x = 4y + 3 equation 1st

→ y = -2x -3 equation 2nd .

Now putting the value of x from first equation to second equation.

→ y = -2(4y +3 ) -3

→ y = -8y - 6 - 3

→ y + 8y = -9

→ 9y = -9

→ y = -1

Now putting the value of y in equation first .

→ x = 4(-1) + 3

→ x = -4 + 3

→ x = -1

Now multiply and X and y.

→ x.y = -1(-1)

→ x.y = 1 .

[tex]\huge {\bold {\star {\fcolorbox {black} {yellow} {Answer}}}} [/tex]

Putting the value of x in ii, we get ;

➝ y = - 2(4y+3) - 3

➝ y = - 8y - 6 - 3

➝ y = - 8y - 9

➝ y + 8y = - 9

➝ 9y = - 9

∴ y = - 1

Putting the value of y in i, we get ;

➝ x = 4y + 3

➝ x = 4(-1) + 3

➝ x = - 4 + 3

∴ x = - 1

➛ xy = (- 1)(-1)

⛬ xy = 1

Hi there! :)

Answer:

[tex]\huge\boxed{L = 9 \text { units}}[/tex]

Given:

Perimeter = 28

Let the breadth = x. The length is 4 units greater, so we can represent this as (x + 4).

Set up an expression. Remember that the formula for the perimeter of a rectangle is:

P = 2(l) + 2(w)

Substitute:

28 = 2(x) + 2(x+ 4)

Distribute:

28 = 2x + 2x + 8

Combine like terms and simplify:

28 = 4x + 8

20 = 4x

x = 5.

The length of the breadth is 5 units. Substitute in 5 to solve for the length:

(5) + 4 = 9 units.

The length of the rectangle is 9 units.

Answer:

B

Step-by-step explanation:

The clock at six o clock form a line:

         12

           |

9         |           3

           |

          6

Answer:

1/-30

Step-by-step explanation:

5/6/-5/6

= 5/6 x 6/-5

= 5/30 x 6/-30

= 30/-900

= 1/-30

Answer:

RHS=tanA/2

Step-by-step explanation:

LHS=1+sinA-cosA/1+sinA+cosA

=(1-cosA)+sinA/(1+cos A)+sinA

=2sin^2A/2+2sinA/2*cosA/2

_____________________

2cos^2A/2+22sinA/2*cosA/2

=2sinA/2(sinA/2+cosA/2)

___________________

2cosA/2(sinA/2+cosA/2)

sinA/2

=_____

cosA/2

= tanA/2 proved.

Answer:  see proof below

Step-by-step explanation:

Use the following Double Angle Identities:

sin 2A = 2cos A · sin A

cos 2A = 2 cos²A - 1

Use the following Quotient Identity: tan A = (sin A)/(cos A)

Use the following Pythagorean Identity:

cos²A + sin²A = 1   -->   sin²A = 1 - cos²A

Proof LHS → RHS

Given:                            [tex]\dfrac{1+sin\theta - cos \theta}{1+sin \theta +cos \theta}[/tex]

Let Ф = 2A:                    [tex]\dfrac{1+sin2A - cos 2A}{1+sin2A +cos2A}[/tex]

Un-factor:                       [tex]\dfrac{\bigg(\dfrac{1- cos^2\ 2A}{1+cos\ 2A}\bigg)+sin\ 2A }{1+sin\ 2A +cos\ 2A}[/tex]

Pythagorean Identity:   [tex]\dfrac{\bigg(\dfrac{sin^2\ 2A}{1+cos\ 2A}\bigg)+sin\ 2A }{1+cos\ 2A +sin\ 2A}[/tex]

Simplify:                          [tex]\dfrac{sin\ 2A}{1+cos\ 2A}[/tex]

Double Angle Identity:   [tex]\dfrac{2sin\ A\cdot cos\ A}{1+(2cos^2 A-1)}[/tex]

Simplify:                          [tex]\dfrac{2sin\ A\cdot cos\ A}{2cos^2\ A}[/tex]

                                   [tex]=\dfrac{2sin\ A\cdot cos\ A}{2cos^2\ A}[/tex]

                                   [tex]=\dfrac{sin\ A}{cos\ A}[/tex]

Quotient Identity:       tan A

[tex]\text{Substitute} A = \dfrac{\theta}{2}}:\qquad tan\dfrac{\theta}{2}[/tex]

[tex]tan\dfrac{\theta}{2} = tan\dfrac{\theta}{2}\quad \checkmark[/tex]

Answer:

we

Step-by-step explanation:

ee

Answer:

x = -6 y = 3

Step-by-step explanation:

Adding the two equations and you get, -3x-3y + 3x+8y= 6+9

=> 5y = 15

=> y = 3

Plug y in each equation

-3x -3(3) = 9

-3x -9 = 9

-3x = 18

x = -6

3x + 8(3) = 6

3x +24 = 6

3x = -18

x = -6

The theoretical probability of getting heads is; 12%

We are given;

Number of times coin is flipped = 20 times

Number of heads gotten = 12 heads

Number of tails gotten = 8

Assuming the coin is fair, then;

p = 0.5 and q = 0.5

Using binomial probability formula we have;

P(getting heads) = ²⁰C₁₂ * 0.5¹² * 0.5⁽²⁰ ⁻ ¹²⁾

P(getting heads) = 125970 * 0.00000095367431640625

P(getting heads) = 0.12 or 12%

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Answer:

-577

Step-by-step explanation:

−4 − 6 + 2 + 5 + 8 − 3 (8 − 6 − 3) − (−6 − 2 − 5) (9 − 4)(−6 − 3)

Answer:

Add 12 to the product of 13 and a number p.

Step-by-step explanation:

Given expression: 13p + 12

In the expression, 13 is multiplied by a number p, and 12 is added to the result. Therefore, a simple word phrase for the given expression would be: Add 12 to the product of 13 and a number p.

i.e 13 × p = 13p

Then add 12,

     =  13p + 12

Answer:

ummm

Step-by-step explanation:

look it up

I'm helping you look it up right now

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Statement 1: [tex]\angle 2[/tex] and [tex]\angle 4[/tex] are vertical angles

Reason 1: Given

We basically just restate the given information word for word. This is true of any two column proof.

-------------------------------------

Statement 2:  [tex]m \angle 2 + m \angle 3 = 180[/tex]

Reason 2: [tex]\angle 2[/tex] and [tex]\angle 3[/tex] are a linear pair

The term "linear pair" means the angles are adjacent and supplementary (they form a straight line), so this is why the two angles add to 180.

--------------------------------------

Statement 3: [tex]m \angle 3 + m \angle 4 = 180[/tex]

Reason 3: [tex]\angle 3[/tex] and [tex]\angle 4[/tex] are a linear pair

--------------------------------------

Statement 4: [tex]m \angle 2 + m \angle 3 = m \angle 3 + m \angle 4[/tex]

Reason 4: Substitution

Each of the equations formed in statements 2 and 3 above have 180 on the right side, so the left hand sides must be the same

--------------------------------------

Statement 5: [tex]m \angle 2 = m \angle 4[/tex]

Reason 5: Subtraction property of equality

We subtracted the quantity [tex]m \angle 3[/tex] from both sides (they go away)

--------------------------------------

Statement 6: [tex]\angle 2 \cong \angle 4[/tex]

Reason 6: Definition of congruence

If two items are congruent, then they have the same measure. In other words, they are the same.

The proof of  [tex]\angle 2 \ and \ \angle4[/tex] are vertical angles is explained below.

Given, [tex]\angle 2 \ and \ \angle4[/tex] are vertical angles as shown in fig.

We know that, Vertical angles are formed when two straight lines intersect at a point.Vertical angles are two angles which are vertically opposite and have the same measure. So, the two angles are to be congruent.

We have to prove that angle 2 and angle 4 congruent.

Given [tex]\angle 2 \ and\ \angle 3[/tex] makes linear pair so,  

[tex]\angle 2+\angle 3= 180[/tex]

[tex]\angle 3 =180-\angle 2[/tex]..........(1)

Again [tex]\angle 3 \ and \ \angle 4[/tex] makes linear pair so,

[tex]\angle 3+\angle 4= 180[/tex]

[tex]\angle 3 =180-\angle 4[/tex].......(2)

From (1) and (2) we get,

[tex]180-\angle 2=180-\angle 4[/tex]

Subtracting 180 from both the sides we get,

[tex]-\angle 2=-\angle 4[/tex]

Or, [tex]\angle 2=\angle 4[/tex]

Hence angle 2 and angle 4 are congruent.

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Answer:

The answer is

Step-by-step explanation:

The midpoint M of two given points is given by

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(10,5) and (-2, -10)

The midpoint of points is

We have the final answer as

Hope this helps you

Answer:

- 7 - i

Step-by-step explanation:

Given

(- 10 - 2i) + (3 + i) ← remove parenthesis

= - 10 - 2i + 3 + i ← collect like terms

= - 7 - i

Answer: 7

Explanation:

List out the factors of 120 until we hit a gap

1,2,3,4,5,6,8

Note that 7 is not shown above. We can see that 120/7 = 17.14 approximately meaning that 7 doesn't go evenly into 120. So this is why 7 isn't a factor. Something like 3 is a factor because 120/3 = 40 is a whole number result.

Also, 7 is prime. The only factors of 7 are 1 and itself. This means that 7 and 120 do not have any common factors other than 1. The GCF of 7 and 120 is 1, leading to the two numbers being relatively prime

Side note: The term "coprime" is sometimes used in place of "relatively prime"

Answer:

2.4

Step-by-step explanation:

Answer is  2.4

Answer:

12/5

Step-by-step explanation:

Answer:

  4,834

Step-by-step explanation:

  $14,500/($3 / pizza) = 4833.3 pizzas

MOD Pizza must sell 4,834 pizzas to cover the cost of the oven.

Answer:

13 m

Step-by-step explanation:

The ladder forms a right triangle with the wall that has legs of 5 and 12. We need to solve for the length of the ladder, which in this case, is the hypotenuse of the right triangle. You could use the Pythagorean Theorem but there's an easier way to do this. We can use the 5 - 12 - 13 Pythagorean triple so we know that the length of the ladder is 13 m.

Answer:

B. sen α = BC/b

Step-by-step explanation:

Las identidades trigonométricas se utilizan para resolver problemas de ángulos rectos.

En un ángulo recto, el lado al que se hace referencia como opuesto es el lado opuesto al ángulo, el lado al que se hace referencia como adyacente es el lado siguiente al ángulo (entre el ángulo y el ángulo recto) mientras que la hipotenusa es el lado más largo (opuesto al ángulo recto)

De identidades trigonométricas:

[tex]sen\ \alpha=\frac{lado\ opuesto}{hipotenusa} \\\\lado\ opuesto=BC=a\\\\hipotenusa=b\\\\sen\ \alpha=\frac{lado\ opuesto}{hipotenusa} =\frac{BC}{b} \\\\sen\ \alpha =\frac{BC}{b}[/tex]

Answer:

His average rate of speed for the entire trip is 10 miles/hour.

Step-by-step explanation:

We are given that John went on a bike ride to the store 4 miles away. If it took John 3/10 of an hour to get there and 1/2 of an hour to get back.

And we have to find his average rate of speed (miles per hour) for the entire trip.

As we know that the Distance-Speed-Time formula is given by;

                    [tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]  

Here, the distance for the entire trip = 8 miles (4 miles for reaching store and 4 miles for returning back)

The time taken for the entire trip = [tex](\frac{3}{10} )[/tex] of an hour to reach the store and [tex](\frac{1}{2})[/tex] an hour to get back.    

So, the average rate of speed for the entire trip = [tex]\frac{\text{Total Distance}}{\text{Total Time}}[/tex]

                             =  [tex]\frac{8}{\frac{3}{10}+\frac{1}{2} }[/tex]

                             =  [tex]\frac{8}{\frac{8}{10} }[/tex]  =  10 miles per hour

Hence, his average rate of speed for the entire trip is 10 miles/hour.

Answer:

  15 kg

Step-by-step explanation:

We can multiply the given ratio units by 6 to make them be integers:

  (1/2) : (1/3) = 3 : 2

Then we can see that the second man has 2/3 the weight of the first man.

  (2/3)(22.5 kg) = 15 kg

The second person weighs 15 kg.

Answer:

The data is skewed to the bottom and contains an outlier.  

Step-by-step explanation:

1. Test for outlier

An outlier is a point that is more than 1.5IQR below Q1 or above Q3.  

IQR = Q3 - Q1 = 74 - 51 = 23

1.5 IQR  = 1.5 × 23 = 34.5

51 - 15 = 36 > 1.5IQR

The point at 15 is an outlier.

2. Test for normal distribution

The median is not in the middle of the box.  

Rather, it cuts the box into two unequal parts, so the data does not have a normal distribution.

3. Test for skewness

The longer part is to the left of the median, so the data is skewed left.

Answer:

5A: All you got to do is put in the number of videos (v) and figure the equation out. For example,  40 x 20 + 3v = $803v.

I really hope this helps you!